Algorithms, systems, and methods for estimating carbon dioxide stores, transforming respiratory gas measurements, and obtaining accurate noninvasive pulmonary capillary blood flow and cardiac output measurements

ABSTRACT

Methods for estimating the volume of the carbon dioxide stores of an individual&#39;s respiratory tract include determining a carbon dioxide store volume at which a correlation between corresponding signals of carbon dioxide elimination and an indicator of the content of carbon dioxide in blood of the individual is optimized. The estimate of the volume of carbon dioxide stores, which comprises a model of the respiratory tract, or lungs, of the individual, may be used as a transformation to improve the accuracy of one or both of the carbon dioxide elimination and carbon dioxide content signals. Transformation, or filtering, algorithms are also disclosed, as are systems in which the methods and algorithms may be used. The methods, algorithms, and systems may be used to accurately and noninvasively determine one or both of the pulmonary capillary blood flow and cardiac output of the individual.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 10/121,219,filed Apr. 11, 2002, now U.S. Pat. No. 6,995,651, issued Oct. 18, 2005,which is a continuation-in-part of U.S. application Ser. No. 09/510,702,filed on Feb. 22, 2000, now U.S. Pat. No. 6,540,689, issued Apr. 1,2003.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to methods for noninvasivelydetermining the pulmonary capillary blood flow or cardiac output of anindividual. More specifically, the present invention relates tononinvasive methods for determining pulmonary capillary blood flow orcardiac output which account for correlation between parameters thathave been measured during the same breath. In particular, the presentinvention includes methods for improving the correlation between carbondioxide elimination and partial pressure of end-tidal carbon dioxidemeasurements.

2. Background of Related Art

So-called “rebreathing” techniques have long been used to makenoninvasive determinations of both pulmonary capillary blood flow andcardiac output. In rebreathing, the respiration of an individual ismonitored during both “normal” breathing, which may be eitherspontaneous or ventilator-induced, and when a change in the effectiveventilation of the individual has occurred or been induced. Inparticular, in conventional rebreathing techniques, the change ineffective ventilation has been induced by causing a monitored individualto breathe air or a gas mixture with an increased level of carbondioxide relative to the amount of carbon dioxide that was inhaled by theindividual during “normal” breathing.

The carbon dioxide Fick equation has long been used to determine bothpulmonary capillary blood flow and cardiac output. One form of thecarbon dioxide Fick equation follows:{dot over (Q)}=VCO ₂/(c _(vCO2) −c _(aCO2)),  (1)where {dot over (Q)} represents blood flow (e.g., cardiac output orpulmonary capillary blood flow), VCO₂ is carbon dioxide elimination,c_(vCO2) is carbon dioxide content of the venous blood of the monitoredindividual, and c_(aCO2) is the carbon dioxide content of the arterialblood of the monitored individual.

When rebreathing processes are employed, the various parameters of thecarbon dioxide Fick equation are typically derived from two measuredsignals, a measurement of the volume or flow of carbon dioxideeliminated by the body (VCO₂ and {dot over (V)}CO₂, respectively), whichrepresents gases that are present in the mouth, and a measurement of thepartial pressure of end-tidal carbon dioxide (_(etCO2) or p_(etCO2)),which represents gases inside the lungs, at the alveoli. The p_(etCO2)measurement correlates directly with a concentration of carbon dioxidein blood flowing past the alveoli of an individual (c_(ACO2)) and,therefore, is useful for determining c_(aCO2) and c_(vCO2).

Rebreathing is often conducted with a rebreathing circuit, through whicha patient may inhale a gas mixture that includes carbon dioxide. FIG. 1schematically illustrates an exemplary rebreathing circuit 50 thatincludes a tubular airway 52 that communicates air flow to and from thelungs of a patient. Tubular airway 52 may be placed in communicationwith the trachea of the patient by known intubation processes, or byconnection to a breathing mask positioned over the nose and/or mouth ofthe patient. A flow meter 72, which is typically referred to as apneumotachometer, and a carbon dioxide sensor 74, which is typicallyreferred to as a capnometer, are disposed between tubular airway 52 anda length of hose 60, and are exposed to any air that flows throughrebreathing circuit 50. Flow meter 72 and carbon dioxide sensor 74communicate with one or more monitors 76, which are configured tomonitor signals from flow meter 72 and carbon dioxide sensor 74, asknown in the art. Both ends of another length of hose, which is referredto as deadspace 70, communicate with hose 60. The two ends of deadspace70 are separated from one another by a two-way valve 68, which may bepositioned to direct the flow of air through deadspace 70. Deadspace 70may also include an expandable section 62. A Y-piece 58, disposed onhose 60 opposite flow meter 72 and carbon dioxide sensor 74, facilitatesthe connection of an inspiratory hose 54 and an expiratory hose 56 torebreathing circuit 50 and the flow communication of the inspiratoryhose 54 and expiratory hose 56 with hose 60. During inhalation, gasflows into inspiratory hose 54 from the atmosphere or a ventilator (notshown). During normal breathing, valve 68 is positioned to preventinhaled and exhaled air from flowing through deadspace 70. Duringrebreathing, valve 68 is positioned to direct the flow of exhaled andinhaled gases through deadspace 70.

The rebreathed air, which is inhaled from deadspace 70 duringrebreathing, includes air that has been exhaled by the patient (i.e.,carbon dioxide-rich air).

During total rebreathing, substantially all of the gas inhaled by thepatient was expired during the previous breath. Thus, during totalrebreathing, the partial pressure of end-tidal carbon dioxide (p_(etCO2)or _(etCO2)) is typically assumed to be equal to or closely related tothe content of carbon dioxide in the arterial (c_(aCO2)), venous(c_(vCO2)), or alveolar (c_(ACO2)) blood of the patient. Totalrebreathing processes are based on the assumption that neither pulmonarycapillary blood flow nor the content of carbon dioxide in the venousblood of the patient (c_(vCO2)) changes substantially during therebreathing process. In total rebreathing, the carbon dioxideelimination (VCO₂) of the patient decreases to about zero. The partialpressure of carbon dioxide in blood may be converted to the content ofcarbon dioxide in blood by means of a carbon dioxide dissociation curve,where the change in the carbon dioxide content of the blood(C_(yCO2)−C_(aCO2)) is equal to the slope(s) of the carbon dioxidedissociation curve multiplied by the measured change in end-tidal carbondioxide (p_(etCO2)) as effected by a change in effective ventilation,such as rebreathing.

In partial rebreathing, the patient inhales gases that include elevatedcarbon dioxide levels (e.g., a mixture of “fresh” gases and gases thatwere exhaled during the previous breath). Thus, the patient does notinhale a volume of carbon dioxide as large as the volume of carbondioxide that would be inhaled during a total rebreathing process. Ascarbon dioxide elimination (VCO₂) is not decreased to zero duringpartial rebreathing and since the carbon dioxide content of the mixedvenous blood is not known during partial rebreathing, partialrebreathing processes typically employ a differential form of the carbondioxide Fick equation to determine the pulmonary capillary blood flow orcardiac output of the patient. This differential form of the carbondioxide Fick equation considers measurements of carbon dioxideelimination, c_(vCO2), and the content of carbon dioxide in the alveolarblood of the patient (c_(ACO2)) during both normal breathing and therebreathing process as follows:

$\begin{matrix}{{\overset{.}{Q}}_{{pcb}\mspace{14mu}{BD}} = \frac{{VCO}_{2\mspace{14mu} B} - {VCO}_{2\mspace{11mu} D}}{{\left( {c_{{vCO2}\mspace{14mu} B} - c_{{vCO2}\mspace{14mu} D}} \right) - \left( {c_{{aCO2}\mspace{14mu} B} - c_{{aCO2}\mspace{14mu} D}} \right)},}} & (2)\end{matrix}$where VCO_(2 B) and VCO_(2 D) are the carbon dioxide production of thepatient before rebreathing and during the rebreathing process,respectively, c_(vCO2 B) and c_(vCO2 D) are the content of CO₂ of thevenous blood of the patient before rebreathing and during therebreathing process, respectively, and c_(aCO2 B) and c_(aCO2 D) are thecontent of CO₂ in the arterial blood of the patient before rebreathingand during rebreathing, respectively.

Again, with a carbon dioxide dissociation curve, the measured p_(etCO2)can be used to determine the change in content of carbon dioxide in theblood before and during the rebreathing process. Accordingly, thefollowing equation can be used to determine pulmonary capillary bloodflow or cardiac output when partial rebreathing is conducted:{dot over (Q)}=ΔVCO₂ /sΔp _(etCO2).  (3)

Accordingly, a plot of VCO₂ against p_(etCO2) during both “normal”respiration and rebreathing is known to provide an indicator of thepulmonary capillary blood flow of an individual. The individual'spulmonary capillary blood flow is about equal to the negative slope(i.e., negative one multiplied by the slope) of the resulting line orcurve.

Alternative differential Fick methods of measuring pulmonary capillaryblood flow or cardiac output have also been employed. Such differentialFick methods typically include a brief change of p_(etCO2) and VCO₂ inresponse to a change in effective ventilation. This brief change can beaccomplished by adjusting the respiratory rate, inspiratory and/orexpiratory times, or tidal volume. A brief change in effectiveventilation may also be effected by adding CO₂, either directly or byrebreathing. An exemplary differential Fick method that has beenemployed, which is disclosed in Gedeon, A. et al. in 18 MED. & BIOL.ENG. & COMPUT. 411–418 (1980), includes a period of increasedventilation followed immediately by a period of decreased ventilation.

Carbon dioxide elimination (VCO₂) is typically measured as thedifference between the amount of carbon dioxide inhaled and the amountof carbon dioxide exhaled, with the amount of carbon dioxide exhaledusually being greater than that inhaled. The carbon dioxide eliminationof a patient is typically measured over the course of a breath by thefollowing, or an equivalent, equation:VCO ₂=∫_(breath) V×f _(CO2) dt,  (4)where V is the measured respiratory flow and f_(CO2) is thesubstantially simultaneously detected carbon dioxide signal, or fractionof the respiratory gases that comprises carbon dioxide or “carbondioxide fraction.”

Prior to rebreathing, the amount of carbon dioxide eliminated (VCO₂) bythe patient, through his or her lungs, is much greater than the amountof CO₂ inhaled by the patient. In rebreathing, although the amount ofcarbon dioxide inhaled by the individual and the amount of carbondioxide exhaled by the individual both typically increase, the VCO₂measurement typically decreases. The difference between the amounts ofcarbon dioxide inhaled and eliminated is reduced by an amount thatcorresponds to the increased amount of carbon dioxide inhaled by thepatient. Detection of the change in VCO₂ that may occur with changes inthe effective ventilation of an individual may be somewhat delayed dueto the dampening effect of the carbon dioxide stores of the individual'slungs. For example, at the beginning of rebreathing, a significantportion of the increased amount of carbon dioxide inhaled by theindividual is absorbed by the carbon dioxide stores. If the amount ofcarbon dioxide inhaled during rebreathing is significantly increased,then a significant decrease will be seen in the difference between theamounts of carbon dioxide inhaled and eliminated, while this differencewill be much less if the amount of carbon dioxide inhaled duringrebreathing is only slightly greater than that inhaled during thepatient's normal respiration.

VCO₂ is the first of the two signals (i.e., VCO₂ and p_(etCO2)) toaccurately reflect rebreathing-induced changes. When rebreathing isinitiated, the amount of carbon dioxide that is inhaled is increased.Prior to rebreathing, the lungs of the patient have been exposed totypical amounts of carbon dioxide, such as those experienced duringnormal respiration. Initially, some of the increased carbon dioxide thatis inhaled during rebreathing is absorbed by the carbon dioxide storesof the lungs, including the functional residual capacity (FRC), whichcomprises stored gases, and lung tissues. Thus, only a portion of theincreased amount of inhaled carbon dioxide initially makes its way tothe alveoli, or air sacs, of the lungs, where gases exit and areabsorbed by the blood. It only takes a short amount of time for thecarbon dioxide stores of the lungs to equilibrate to the increasedamount of carbon dioxide being inhaled. When such equilibration occurs,substantially all of the increase in the amount of carbon dioxideinhaled is realized in the alveoli. At that point in time, the fullreduction in the difference between the amount of carbon dioxide inhaledby the patient and the amount of carbon dioxide eliminated by thepatient may be noninvasively measured.

Assuming the increased amount of carbon dioxide inhaled by theindividual is sufficient to quickly maximize the concentration of carbondioxide in the carbon dioxide stores, the amount of carbon dioxideexhaled by the individual in the same breath may be used to accuratelydetermine the VCO₂ of the patient.

The partial pressure of end-tidal carbon dioxide (p_(etCO2) or_(etCO2)), after correcting for any deadspace, is typically assumed tobe approximately equal to the partial pressure of carbon dioxide in thealveoli (PACO₂) of the patient or, if there is no intrapulmonary shunt,the content of CO₂ in the blood flowing past the alveoli (c_(ACO2)), aswell as the CO₂ content of oxygenated blood downstream from the alveoli(c_(aCO2)).

The p_(etCO2) measurement, which represents a measurement of carbondioxide in the lungs of an individual, is typically not representativeof the true gases that are present in the lungs at the time themeasurement is taken. This is because, in rebreathing, the increasedamount of carbon dioxide inhaled does not go directly to the alveoli.Rather, the carbon dioxide stores of the lungs, including the functionalresidual capacity (deadspace) and lung tissues, which do not participatedirectly in respiration, act as a buffer or filter. This filteringaction includes the absorption and release of carbon dioxide in a mannerthat depends upon the amount of carbon dioxide in gases that aredirectly involved in respiration. Accordingly, when rebreathing firstbegins, a significant portion of the increased amount of carbon dioxidein the inhaled gases is initially absorbed into the carbon dioxidestores. Once the amount of carbon dioxide in the carbon dioxide storesand the amount of carbon dioxide in the “rebreathed” gases (includinginspiratory and expiratory gases) equilibrate with one another, theamount of carbon dioxide within the lungs, including p_(etCO2), may beaccurately detected. The converse is also true: when “normal”respiration is recommenced, the reduced amount of carbon dioxide in theexpired gases is not immediately realized in an externally obtained,noninvasive respiratory measurement. Rather, carbon dioxide is releasedfrom the carbon dioxide stores of the lungs until the amount of carbondioxide in the carbon dioxide stores equilibrates with the amounts ofcarbon dioxide in the inspiratory and expiratory gases. Only after suchequilibration has taken place may accurate measurements of gases withinthe lungs, such as p_(etCO2), be noninvasively obtained. Accordingly, atthe start of both a rebreathing phase and “normal” breathing following arebreathing phase, an immediate change in p_(etCO2) is typically notseen.

Once the increase in the amount of inhaled carbon dioxide is realized atthe level of the alveoli, the content of CO₂ in the blood must increasecorrespondingly for carbon dioxide to be released from the blood as theblood flows past the alveoli. Thus, an additional period of time isrequired before the amount of carbon dioxide in the blood increases to alevel which will facilitate release of the increased amount of carbondioxide from the blood and an increase in the amount of carbon dioxidein the blood, which may be determined from a p_(etCO2) measurement, maybe detected. Thus, the accuracy of the p_(etCO2), relative to the pointin time at which the measurement is obtained relative to the initiationof rebreathing, lags behind the time-accuracy of the VCO₂ measurement.This lag typically amounts to a period of time that corresponds to oneor two breaths.

Following rebreathing, the amount of carbon dioxide inhaled by a patientis decreased. The carbon dioxide stores in the lungs equilibrate to thenew amount of carbon dioxide being inhaled by releasing carbon dioxide.Consequently, while the carbon dioxide levels of the carbon dioxidestores of the lungs are equilibrating, the amount of carbon dioxideexhaled by the patient remains at an elevated level for a period of timefollowing even a significant decrease in the amount of carbon dioxideinhaled by the patient.

Likewise, during equilibration of the carbon dioxide stores of apatient's lungs, the amount of carbon dioxide within the alveoli remainsgreater than that in the air or other gas mixture inhaled by thepatient. Thus, carbon dioxide levels in the blood remain elevated. Oncethe carbon dioxide stores in the lungs of the patient begin to decreaseand the amount of carbon dioxide within the alveoli begins to resemblethe amount of carbon dioxide in the air or gases that have been inhaledby the patient, the high levels of carbon dioxide that have accumulatedin the blood may be more readily released therefrom. Accordingly,following rebreathing, the amount of carbon dioxide in the blood flowingpast the alveoli of the patient will initially remain high, as may beevidenced by relatively high p_(etCO2) measurements. As the excesscarbon dioxide that is trapped in the blood during rebreathing isgradually released therefrom, the amount of carbon dioxide in thealveolar blood of the patient decreases to a “normal” level.

It may be said that the carbon dioxide stores of a patient's lungsfilter the p_(etCO2) signal to a much greater extent than the VCO₂signal is filtered by the carbon dioxide stores. Because VCO₂ signalstypically respond to changes in the effective ventilation of a patient,such as rebreathing and nonrebreathing states, about one or two breathsbefore the p_(etCO2) signal(s) for the same breath(s) will respond tosuch changes, VCO₂ and p_(etCO2) signals that are obtained during thesame breath do not correlate well with one another. Accordingly, a VCO₂signal may lead a p_(etCO2) signal by a time differential equal to theduration of about one or two breaths. Thus, at a particular point intime, the VCO₂ and p_(etCO2) signals do not correspond to one another.Stated another way, the accuracy of the p_(etCO2) measurement lags thatof the VCO₂ measurement by a time duration equal to the length of abreath or two. As these values are often used to noninvasively determinepulmonary capillary blood flow or cardiac output, the lack ofcorrespondence between these values may lead to inaccuracies in thepulmonary capillary blood flow or cardiac output determination.

The correlation between the p_(etCO2) and VCO₂ signals may be quantifiedby a so-called “correlation coefficient” (r²), where a value of 1indicates complete correlation between the two signals and lesser valuesrepresent correspondingly lesser degrees of correlation. This isevidenced when VCO₂ signals are plotted against c_(aCO2) signals, suchas the data shown in FIGS. 2A and 2B respectively, with the resultappearing as an open loop, as depicted in the plot of FIG. 4, ratherthan the ideal straight line depicted in FIG. 3. As it is difficult toaccurately assign a slope to a loop, it is difficult to accuratelydetermine pulmonary capillary blood flow from a plot of noninvasivelyobtained p_(etCO2)-based c_(aCO2) signals against VCO₂ signals.

Upon the start of rebreathing, the flow of carbon dioxide eliminated atthe mouth ({dot over (V)}_(M)CO₂) almost instantaneously drops to alower level, while the plot of p_(etCO2) goes through a transitionalperiod before reaching the steady-state plateau at which it stays untilthe end of rebreathing. The trend plots of alveolar CO₂ content(C_(ACO2)) and the volume of CO₂ excreted from the blood into thealveoli ({dot over (V)}_(B)CO₂) from the carbon dioxide Fick equation(equation (1)) should follow the same shape (albeit inverted, due to thenegative slope) as that of FIG. 3. However, VCO₂ is not measured at thealveolar level ({dot over (V)}_(B)CO₂), but at the mouth ({dot over(V)}_(M)CO₂).

In addition, measurements that are taken during spurious breaths, orbreaths which do not provide information relevant to pulmonary capillaryblood flow or cardiac output, may act as noise that introducesinaccuracy into the noninvasive pulmonary capillary blood flow orcardiac output determination.

When equation (4) is employed to calculate the VCO₂ of a patient fromthe respiratory flow and carbon dioxide fraction measurements over anentire breath, such miscorrelation or noise-induced inaccuracies ineither the expiratory flow, the inspiratory flow, or both may causeinaccuracies in the determination of VCO₂ or inconsistencies betweenVCO₂ determinations.

The inventors are not aware of a method for using a model of the lungwhich includes estimation, evaluation, or use of the carbon dioxidestores of the lung to transform, modify, or filter one or morenoninvasively obtained respiratory signals to increase the correlationof each filtered or modified respiratory signal with at least one othernoninvasively obtained respiratory signal.

SUMMARY OF THE INVENTION

The present invention includes correlating an indicator of a change inVCO₂, which, for simplicity, is hereinafter referred to as a “change inVCO₂,” to a corresponding change in an indicator of the content ofcarbon dioxide in the blood. Examples of changes in VCO₂ that may beobtained and transformed in accordance with teachings of the presentinvention include, without limitation, a change in the net volume of CO₂(between expiratory and inspiratory CO₂), a change in the inspiratoryvolume of CO₂, and a change in another component of inspired or expiredair (e.g., a change in oxygen). Examples of changes in an indicator ofthe content of CO₂ in the blood of an individual include, but are notlimited to, c_(vCO2), c_(ACO2), c_(aCO2), and p_(etCO2), as well assurrogates and equivalents of any of the foregoing. Correlation inaccordance with teachings of the present invention may be used inaccurately and noninvasively measuring the pulmonary capillary bloodflow or cardiac output of an individual.

In an exemplary aspect of the present invention, one or both of the VCO₂and p_(etCO2) signals that have been taken at different respiratory orventilatory states may be transformed or filtered, such as over thecourse of a change in the effective ventilation of an individual (e.g.,during a rebreathing process). Transformation or filtering in accordancewith teachings of the present invention effectively counteracts anydampening by the carbon dioxide stores in the lungs of an individualover the course of a change in the effective ventilation of theindividual and substantially correlates VCO₂ and p_(etCO2) signals thatcorrespond, in time, to one another. Stated another way, the shapes ofcorresponding VCO₂ and p_(etCO2) or c_(CO2) signals may be compared withone another to estimate the size or effect of the lung stores on theaccuracies of these measurements and, thus, to determine an appropriatetransformation coefficient, or filter coefficient, for increasing theaccuracy of one or more of the VCO₂, p_(etCO2), and c_(CO2) signals.Methods of the present invention may, therefore, substantially eliminateany lag time that may be caused by carbon dioxide stores of anindividual's lungs and that may exist between changes in the amounts ofrespiratory gases at the mouth and those in the lungs.

By way of example only and not to limit the scope of the presentinvention, the p_(etCO2) signal, which tends to be dampened, orfiltered, by the carbon dioxide stores of an individual's lungs to agreater degree than a VCO₂ signal obtained from respiration of theindividual, may be “sped up” to match a corresponding VCO₂ signal. Thep_(etCO2) signal may be “sped up” by amplifying the signal.

As another example, the VCO₂ or {dot over (V)}CO₂ signal may be “sloweddown.” Slowing down of the VCO₂ signal may be accomplished by use of asignal from at least one previous or subsequent breath, such as thebreath that immediately preceded that from which a “corresponding”p_(etCO2) signal has been obtained. Use of this technique may facilitatethe effective elimination of any noise that may be present in a VCO₂ or{dot over (V)}CO₂ signal.

As the difference in the rates at which the carbon dioxide stores of anindividual's lungs dampen, or filter, the p_(etCO2) and VCO₂ signals istaken into consideration in the method of the present invention, it maybe said that the method of the present invention employs a model of thelung of an individual to measure the individual's p_(etCO2).

The volume of carbon dioxide stores in the lungs of the individual,including the so-called functional residual capacity, or gas volume ofthe lungs that does not directly participate in respiration, and thevolume of carbon dioxide absorbed by the tissues of the lung areestimated to provide a correlation coefficient (referring to thecorrelation between simultaneously obtained VCO₂ and p_(etCO2) signals),or r² value, in which the measured VCO₂ and p_(etCO2) values may beplotted in a substantially linear fashion. Initially, by way of exampleonly, this volume may comprise an estimate based on a size of thepatient or, simply, a prespecified starting point. The estimated volumeof carbon dioxide stores may be adjusted. If the adjustments improve thelinearity of the VCO₂ vs. p_(etCO2) plot, the adjustments are being madein the proper manner. If the linearity of the plotted values decreases,it can readily be determined that different, opposite adjustments mayimprove the linearity with which VCO₂ and p_(etCO2) are plotted againstone another.

It may be assumed that the state of the lungs during a particularbreathing cycle (e.g., during an n^(th) breath during the course ofcausing a change in the effective ventilation of an individual) closelyresembles the state of the lungs during the immediately precedingbreathing cycle (e.g., during the n−1^(th) breath during the course ofcausing a change in the effective ventilation of the individual).Accordingly, when a subsequent breathing cycle begins, the initialestimate of the carbon dioxide stores may be the same or substantiallythe same as the final estimate of the volume of carbon dioxide storesused during the previous breathing cycle.

It is possible, however, that the volume of the carbon dioxide stores ofthe lungs of an individual may change over even relatively short periodsof time. For example, movement by the individual from one position toanother may cause the pressure within the lungs to change, which mayalso result in a change in the volume of the carbon dioxide stores ofthe lungs. The effect of such a change may be estimated and accountedfor in the initial estimate of the carbon dioxide stores for asubsequent breathing cycle, or the initial estimate of the carbondioxide stores may remain the same as that for the previous breathingcycle and be quickly adjusted to compensate for such a change in thevolume of the carbon dioxide stores.

It is also within the scope of the present invention to adjustpreviously obtained measurements when a more accurate estimate of thevolume of carbon dioxide stores in the lungs, or lung model, isobtained.

Although the methods described herein are in reference to twomeasurements and two corresponding compartments of the respiratory tractof an individual, like methods which involve measurements thatcorrespond to more than two parts of an individual's respiratory tractand that match measured signals to particular, common points in time arealso within the scope of the present invention.

As a result of transforming or filtering one or both of the VCO₂ andp_(etCO2) signals obtained over a change in the effective ventilation ofan individual in accordance with teachings of the present invention, itmay be possible to determine the location and, thus, the slope of abest-fit line for a plot of the VCO₂/p_(etCO2) signals, or data points,with greater precision and accuracy, leading to a more accurateestimation of one or both of the pulmonary capillary blood flow andcardiac output of the individual.

While the foregoing type of transformation is conducted in the timedomain, corresponding types of transformation, such as a Fouriertransform, may be conducted in the frequency domain.

Additionally, the present invention includes methods, systems, andalgorithms for estimating the volume of the carbon dioxide stores of anindividual's lungs, as well as methods, systems, and algorithms fordetermining the amount of carbon dioxide flowing into and out of thecarbon dioxide stores and for evaluation of the volume of the FRC of theindividual's lungs.

Other features and advantages of the present invention will becomeapparent to those of ordinary skill in the art through a considerationof the ensuing description, the accompanying drawings, and the appendedclaims.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

In the drawings, which depict exemplary embodiments of various aspectsof the present invention:

FIG. 1 is a schematic representation of an exemplary rebreathing circuitthat may be employed with the methods of the present invention;

FIG. 2A is a graph depicting CO₂ excretion ({dot over (V)}_(M)CO₂)measurements taken at various breaths by an individual;

FIG. 2B is a graph depicting measurements of the content of CO₂ in thealveolar blood of the individual (c_(ACO2)), taken at breaths thatcorrespond to those of the graph of FIG. 2A;

FIG. 3 is a graph in which corresponding {dot over (V)}_(B)CO₂ andc_(ACO2) measurements are plotted against one another, illustrating allof the plotted points being located in an ideal, substantially in-linerelation to one another;

FIG. 4 is a graph in which corresponding {dot over (V)}_(M)CO₂ andc_(ACO2) data from FIGS. 2A and 2B are plotted against one another andare arranged in a so-called “loop;”

FIG. 5 is a schematic representation of an alveolus of an individual,illustrating the locations at which various respiratory and blood gasparameters may be determined;

FIG. 6 is a graph that illustrates the volume of gases in the carbondioxide stores of a respiratory tract of an individual (V_(A)) during aseries of respiratory cycles, or breaths;

FIG. 7 is a graph representing an exemplary relationship between anestimate of the volume of gases in the carbon dioxide stores in arespiratory tract of an individual (V_(A)*) and a correlationcoefficient (r²) between corresponding {dot over (V)}_(B)CO₂ andc_(ACO2) data;

FIG. 8A is a graph depicting CO₂ excretion ({dot over (V)}_(M)CO₂)measurements taken at various breaths by an individual that correspondto the data points depicted in FIG. 2A and which have been transformed,filtered, or otherwise corrected in accordance with teachings of thepresent invention;

FIG. 8B is a graph depicting measurements of the content of CO₂ in thealveolar blood of the individual (c_(ACO2)), which correspond to thedata points depicted in FIG. 2B and which have been taken at breathsthat correspond to those of the graphs of FIGS. 2A and 8A;

FIG. 9 is a plot of the transformed {dot over ({circumflex over(V)}_(M)CO₂ data points of FIG. 8A against the c_(ACO2) data points ofFIG. 8B, in which the plotted points are substantially in-line with oneanother;

FIG. 10 is a graph in which noninvasively obtained flow data that weredetermined in accordance with teachings of the present invention arecompared with corresponding flow data obtained by highly accurate,invasive thermodilution techniques, which graph illustrates the highcorrelation between pulmonary capillary blood flow or cardiac outputmeasurements obtained by methods that incorporate teachings of thepresent invention and those obtained by use of thermodilutiontechniques;

FIG. 11 illustrates the differences between corresponding flowmeasurements obtained by methods of the present invention and thoseobtained by thermodilution techniques; and

FIG. 12 is a schematic representation of an example of a monitoringsystem incorporating teachings of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The rate at which blood flows past a particular alveolus of anindividual's lungs may be calculated as the ratio of the flow of CO₂leaving the blood ({dot over (V)}_(B)CO₂), or carbon dioxide excretionfrom the blood, to the CO₂ content difference between the unoxygenated,upstream blood approaching the alveolus (c_(vCO2)) and oxygenated,downstream blood leaving the alveolus (c_(aCO2)). This is the basis forthe carbon dioxide form of the Fick equation that follows:

$\begin{matrix}{\overset{.}{Q} = \frac{{\overset{.}{V}}_{B}{CO}_{2}}{c_{vCO2} - c_{aCO2}}} & (5)\end{matrix}$As gas exchange occurs at the alveolus, the content of CO₂ in blood atthe alveolus (c_(ACO2)) is assumed to be substantially the same as thecontent of CO₂ in blood leaving the alveolus (c_(aCO2)), assuming thatnone of the blood is shunted away from the alveolus. Thus, c_(ACO2) maybe substituted for c_(aCO2) in equation (5).

Substituting c_(ACO2) for c_(aCO2) and rearranging equation (5) for acalculation of {dot over (V)}_(B)CO₂ results in the following:{dot over (V)} _(B)CO₂ =−{dot over (Q)}c _(ACO2) +{dot over (Q)}c_(vCO2).  (6)In a plot of {dot over (V)}_(B)CO₂ signals (y-axis) against c_(ACO2)signals (x-axis) taken at various points during and before or after achange in the effective ventilation of an individual, it can be seenfrom the standard equation for a line, y=mx+b, that the slope (y) of aline taken through the various plotted data points will be −{dot over(Q)}, while {dot over (Q)} c_(vCO2) is the intercept (b).

Equations (5) and (6) are based on the rate at which carbon dioxideleaves, or is eliminated from, the blood at the alveoli ({dot over(V)}_(B)CO₂). If the flow of CO₂ from the blood into the alveoli, orcarbon dioxide excretion ({dot over (V)}_(B)CO₂), could be measured andplotted against c_(ACO2) during rebreathing, data from every breath,including transitional data points, would fall on the line defined byequation (6). Carbon dioxide excretion ({dot over (V)}_(B)CO₂) is notmeasured at the alveolar level, however. Rather, it is measured ascarbon dioxide elimination ({dot over (V)}_(M)CO₂) at the mouth. Thecarbon dioxide elimination measured at the mouth ({dot over (V)}_(M)CO₂)is the sum of the flow of CO₂ excreted from the blood ({dot over(V)}_(B)CO₂) and the flow of CO₂ into or out of the CO₂ stores ({dotover (V)}_(STORES)CO₂). Thus,{dot over (V)} _(B)CO₂ ={dot over (V)} _(M)CO₂ −{dot over(V)}STORESCO₂.  (7)

At the beginning of rebreathing, the CO₂ stores of an individual's lungsabsorb some of the increased CO₂, causing {dot over (V)}_(B)CO₂ tochange more gradually than {dot over (V)}_(M)CO₂ changes. The CO₂ storesof an individual's lungs may be evaluated by use of a model of the lung,such as the simple model of the lung depicted in FIG. 5, in which asingle alveolus 100 and a corresponding pulmonary capillary 102represent the lung. The direction in which blood flows through pulmonarycapillary 102 is represented by arrows 103. The mouth of an individualis represented at reference 106. In the model of FIG. 5, the carbondioxide stores of the lung are depicted, for the purpose of simplicity,as comprising the physical gas volume 104 of the alveolus (V_(A)). Asknown in the art, V_(A) is related to the functional residual capacity(V_(FRC)) of the lung and to tidal volume (V_(T)). In addition to theillustrated contributors to the CO₂ stores of the lung, CO₂ may bedistributed within other stores, such as the alveolar tissues and othertissues of the lung. In addition, the lung model shown in FIG. 5 omitsV_(T)/V_({dot over (Q)}) mismatch and shunting of blood. For modelingpurposes, the mixing of air within the alveolus (including inspiredgases, CO₂ escaping from the blood, flow of CO₂ into and out of the CO₂stores, and gases within the alveolus) is assumed to occurinstantaneously. The effective volume of the CO₂ stores of anindividual's lungs are denoted herein as “V_(A)*.”

In the method of the present invention, a model of the lung, such asthat depicted in FIG. 5, may be evaluated on a breath-by-breath basis.By way of example only, a breath may be delineated as the period fromthe end of one inspiration to the end of the next inspiration, asillustrated in FIG. 6. In addition, FIG. 6 depicts an example of theeffective volume of CO₂ stores in the individual's respiratory tract(e.g., lungs) during the course of respiration.

If the effective volume of CO₂ stores (V_(A)*) does not change frombreath to breath, the flow into and out of the CO₂ stores from onebreath to the next may be expressed as a change in alveolar CO₂ fraction(f_(A)CO₂) (i.e., the fraction of gases in the alveolus that compriseCO₂), or the difference between f_(A)CO₂ for a particular breath(f_(A)CO₂(n)) and f_(A)CO₂ for the previous breath f_(A)CO₂(n−1).Substituting the change in alveolar CO₂ fraction, along with aconsideration of the volume of the CO₂ stores of the individual's lungsand the individual's respiratory rate (RR), for the flow of CO₂ into andout of the carbon dioxide stores ({dot over (V)}_(STORES)CO₂) inequation (7) results in the following:{dot over (V)} _(B)CO₂(n)={dot over (V)} _(M)CO₂(n)+V _(A)*(n)[f_(A)CO₂(n)−f _(A)CO₂(n−1)]RR,  (8)where “n” denotes the current or most recent breath and “n−1” denotesthe previous breath. Equation (8) is particularly useful for estimating{dot over (V)}_(B)CO₂ from {dot over (V)}_(M)CO₂ measurements that areobtained during the transition from nonrebreathing, or “normal”breathing, to rebreathing. An estimate of {dot over (V)}_(B)CO₂ isdenoted herein as {dot over ({circumflex over (V)}_(B)CO₂ and may besubstituted for {dot over (V)}_(B)CO₂ in equation (8).

As it may be assumed that the alveolar CO₂ fraction (f_(ACO2)) isproportional to p_(etCO2), which may be measured by use of a capnometer,the p_(etCO2) measurement may be used, as known in the art, to obtain anf_(ACO2) value for each breath.

The effective volume of the CO₂ stores (V_(A)*) may be adaptivelyestimated, such as by using the linear correlation between {dot over({circumflex over (V)}_(B)CO₂ from equation (8), substituting{circumflex over (V)}_(A)* for V_(A)*, and c_(ACO2) as a guide (seeequation (6)). The more accurately the estimated effective alveolusvolume {circumflex over (V)}_(A)* reflects the actual effective alveolusvolume V_(A)*, the closer the data points of a plot of {dot over({circumflex over (V)}_(B)CO₂ against c_(ACO2) over the course of achange in the effective ventilation of an individual will be to a linerepresentative of the actual pulmonary capillary blood flow or cardiacoutput of the individual. The ideal value for {circumflex over (V)}_(A)*may, therefore, be determined as the value that results in the bestlinear fit between the plotted data (c_(ACO2) against {dot over({circumflex over (V)}_(B)CO₂) and, thus, a maximized correlationcoefficient, or r² value. By way of example only, an adaptive,iterative, or search algorithm of a type known in the art may be used todetermine {circumflex over (V)}_(A)* for which the correlationcoefficient, or r², is maximized. The graph of FIG. 7 shows an exampleof a {circumflex over (V)}_(A)* value at which r² is maximized.

Once an accurate {circumflex over (V)}_(A)* value has been obtained,V_(FRC) may also be estimated or determined, as known in the art.

Equation (8) may be rewritten, as follows, to reflect the use of{circumflex over (V)}_(A)* as an estimate for V_(A)*:{dot over ({circumflex over (V)} _(B)CO₂(n)={dot over (V)}_(M)CO₂(n)+{circumflex over (V)} _(A)*(n)[f _(A)CO₂(n)−f_(A)CO₂(n−1)]RR.  (9)

The foregoing approach (particularly, the use of equation (9)) workswell when an individual is mechanically ventilated (i.e., on arespirator), in which case the respiratory rate and tidal volume of theindividual's respiration are typically substantially stable, whichprovides for a “clean” f_(A)CO₂ signal.

During mixed or spontaneous ventilation, it may be desirable toeliminate any noise that may occur in the f_(A)CO₂ signal when equation(9) is used, as such noise may result in an inaccurate estimation of{dot over ({circumflex over (V)}_(B)CO₂. An algorithm that is lesssensitive to noise than equation (9) may, therefore, also be useful forestimating {dot over ({circumflex over (V)}_(B)CO₂.

Assuming that pulmonary capillary blood flow and cardiac output do notchange from one breath to the next, the carbon dioxide Fick equation(equation (5)) may be rewritten for two successive breaths:

$\begin{matrix}{\overset{.}{Q} = {\frac{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}}{{c_{vCO2}\left( {n - 1} \right)} - {c_{ACO2}\left( {n - 1} \right)}} = \frac{{\overset{.}{V}}_{B}{{CO}_{2}(n)}}{{c_{vCO2}(n)} - {c_{ACO2}(n)}}}} & (10)\end{matrix}$Further, assuming that c_(vCO2) does not change from one breath to thenext, equation (10) may be simplified to:

$\begin{matrix}{\overset{.}{Q} = \frac{{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\overset{.}{V}}_{B}{{CO}_{2}(n)}}}{{c_{ACO2}(n)} - {c_{ACO2}\left( {n - 1} \right)}}} & (7)\end{matrix}$

Measurements of the CO₂ fraction of gases in an individual's alveoli(f_(A)CO₂) may be used in place of the c_(ACO2) measurements of equation(11) when the slope of the CO₂ dissociation curve (s_(CO2)), a standardcurve which illustrates the rate at which CO₂ molecules dissociate fromthe hemoglobin molecules of red blood cells, and barometric pressure(p_(baro)) are also taken into consideration, as known in the art.Accordingly, equation (11) may be rewritten as follows:

$\begin{matrix}{\overset{.}{Q} = \frac{{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\overset{.}{V}}_{B}{{CO}_{2}(n)}}}{s_{CO2}{p_{baro}\left\lbrack {{f_{A}{{CO}_{2}(n)}} - {f_{A}{{CO}_{2}\left( {n - 1} \right)}}} \right\rbrack}}} & (12)\end{matrix}$Solving this expression for the difference in CO₂ fractions(f_(A)CO₂(n)−f_(A)CO₂(n−1)) yields:

$\begin{matrix}{{{f_{A}{{CO}_{2}(n)}} - {f_{A}{{CO}_{2}\left( {n - 1} \right)}}} = \frac{{{\overset{.}{V}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\overset{.}{V}}_{B}{{CO}_{2}(n)}}}{s_{CO2}p_{baro}\overset{.}{Q}}} & (13)\end{matrix}$Substitution of equation (13) into equation (9) results in:

$\begin{matrix}{{{\hat{\overset{.}{V}}}_{B}{{CO}_{2}(n)}} = {{{\overset{.}{V}}_{M}{{CO}_{2}(n)}} + {\frac{{RR}\;{{\hat{\; V}}_{A}^{*}(n)}}{s_{CO2}p_{baro}\overset{.}{Q}}\left\lbrack {{{\hat{\overset{.}{V}}}_{B}{{CO}_{2}\left( {n - 1} \right)}} - {{\hat{\overset{.}{V}}}_{B}{{CO}_{2}(n)}}} \right\rbrack}}} & (14)\end{matrix}$This expression can now be solved for {dot over ({circumflex over(V)}_(B)CO₂(n):

$\begin{matrix}{{{\hat{\overset{.}{V}}}_{B}{{CO}_{2}(n)}} = {{\frac{1}{1 + \frac{{RR}\mspace{11mu}{{\hat{V}}_{A}^{*}(n)}}{s_{CO2}p_{baro}\overset{.}{Q}}}{\overset{.}{V}}_{M}{{CO}_{2}(n)}} + {\frac{\frac{{RR}\mspace{11mu}{{\hat{V}}_{A}^{*}(n)}}{s_{CO2}p_{baro}\overset{.}{Q}}}{1 + \frac{{RR}\mspace{11mu}{{\hat{V}}_{A}^{*}(n)}}{s_{CO2}p_{baro}\overset{.}{Q}}}{\hat{\overset{.}{V}}}_{B}{{CO}_{2}\left( {n - 1} \right)}}}} & (15)\end{matrix}$Structurally, this result represents a first order single-pole low passfilter of the form{dot over ({circumflex over (V)} _(B)CO₂(n)=(1−α){dot over (V)}_(M)CO₂(n)+α{dot over ({circumflex over (V)} _(B)CO₂(n−1),  (16)where α, the transformation coefficient, may be represented as

$\frac{\frac{{RR}\mspace{11mu}{{\hat{V}}_{A}^{*}(n)}}{s_{CO2}p_{baro}\overset{.}{Q}}}{1 + \frac{{RR}\mspace{11mu}{{\hat{V}}_{A}^{*}(n)}}{s_{CO2}p_{baro}\overset{.}{Q}}}$Of course, {dot over (Q)} is an unknown variable, which is not actuallynecessary for determining either α or {circumflex over (V)}_(A)*.Equation (15) merely proves that equation (16) is equivalent to aphysiologic model of the lungs of an individual by which therelationship between VCO₂, c_(CO2), and {dot over (V)}_(STORES)CO₂ maybe evaluated to accurately determine pulmonary capillary blood flow orcardiac output.

The transformation coefficient (α) in equation (16) may be determinediteratively, by using an initial α value, then progressively increasingand/or decreasing the α value to determine the α value that provides anoptimal correlation coefficient (r²), or provides for a plot of VCO₂values against p_(etCO2) or c_(CO2) values with the greatest linearity(as opposed to an open loop). Other alternative methods for determiningan optimal α value include, without limitation, rote searching, globalsearching, gradient searching (e.g., use of a gradient descent searchalgorithm), use of a least mean squares algorithm, use of otherpredetermined equations or sets of predetermined equations, use of atruly adaptive filtering technique, and use of other techniques todetermine the optimal α value, as known in the art. Once an optimal αvalue has been determined, equation (16) may be used in a determinationof the pulmonary capillary blood flow or cardiac output of anindividual.

The algorithm of equation (16) comprises a simple model of the lung thatmay be used to calculate the amount of CO₂ that flows into and out ofthe carbon dioxide stores of the lungs on a “breath-to-breath” basis. Adetermination of {dot over ({circumflex over (V)}_(B)CO₂(n) inaccordance with either of these models may be used in equation (9) and,of course, when a change in the effective ventilation of an individualhas occurred, to determine the pulmonary capillary blood flow or cardiacoutput of the individual.

An example of the result of applying the algorithms of equations (15),(16), and (9) to the data shown in FIGS. 2A and 2B is depicted in FIGS.8A, 8B, and 9. In the {dot over (V)}_(B)CO₂ and c_(ACO2) trend plots ofFIGS. 8A and 8B, respectively, the {dot over (V)}_(B)CO₂ signal appearsto have been “slowed down” to match the corresponding, inverted c_(ACO2)signal. As a result, plotting the {dot over (V)}_(B)CO₂ signal againstthe c_(ACO2) signal, the data points fall more closely to the linepredicted by the carbon dioxide Fick equation (equation (5) and FIG. 3),as shown in FIG. 9.

Turning now to FIG. 12, a schematic representation of a diagnosticsystem 1 incorporating teachings of the present invention isillustrated. Diagnostic system 1 includes, among other things, a tubularairway 52 in communication with the airway A of an individual I, as wellas a flow meter 72 and a carbon dioxide sensor 74 positioned alongtubular airway 52. Flow meter 72 and carbon dioxide sensor 74communicate signals to corresponding monitors 73 and 75, whichcommunicate electronically with a processor 82 of a respiratory monitor80. Processor 82 is programmed to determine at least VCO₂ and p_(etCO2)based on signals communicated thereto from flow meter 72 and carbondioxide sensor 74. In addition, processor 82 may be programmed to usesignals from one or both of flow meter 72 and carbon dioxide sensor 74or calculated parameters (e.g., VCO₂ and p_(etCO2)) in theabove-described algorithms to facilitate the substantially noninvasiveand accurate determination of pulmonary capillary blood flow or cardiacoutput of the individual. Alternatively, such calculations may be mademanually.

EXAMPLE

Using a common protocol, anesthesia was induced in five mongrel dogs(25.8 kg to 42.4 kg) using tiletamine and zolazepam. Each animal wasintubated and mechanically ventilated throughout the experiment.Anesthesia was maintained with halothane and isoflurane. Cardiac outputwas increased during the experiment using dobutamine and decreased usinghalothane, xylazine, or a combination thereof.

A DUALTHERM (B. Braun Medical Inc., Bethlehem, Pa.) pulmonary arterycatheter was placed and used for periodic thermodilution cardiac outputmeasurements. The DUALTHERM catheter uses a dual thermister thatdirectly measured injectate temperature, thereby eliminating errorscaused by faulty injectate temperature measurement. Thermodilutioncardiac output measurements, using about 10 ml of iced saline, weretaken in triplicate every 10 minutes at random times during therespiratory cycle.

{dot over (V)}_(M)CO₂ and p_(etCO2) were recorded using a commerciallyavailable partial rebreathing system (NICO₂®, Novametrix Medical SystemsInc., Wallingford, Conn.). The flow and CO₂ sensors used by therebreathing system were placed in the breathing circuit between theendotracheal tube and the wye piece of the breathing circuit. Partialrebreathing cycles were comprised of a 30 second rebreathing and a 30second recovery period. Rebreathing cycles were run continuously every60 seconds throughout the experiments.

Respiratory data from the NICO₂® monitor were automatically recorded ona personal computer for later analysis. The stored respiratory data wasprocessed using the model-based lung stores compensation methoddescribed above, using equations (12) and (5). The resulting partialrebreathing cardiac output measurements were compared againstsimultaneously collected thermodilution cardiac output measurements.

A total of 96 thermodilution cardiac output measurements, ranging from0.64 to 10.88 L/min, were taken. Regression analysis of the pairedpartial rebreathing and thermodilution measurements, shown in the graphof FIG. 10, gave a correlation coefficient (r²) of 0.966. As depicted inFIG. 11, Bland-Altman analysis showed a bias of −0.059 L/min and astandard deviation of 0.58 L/min (±24% according to Critchley, LAH, etal., A meta-analysis of studies using bias and precision statistics tocompare cardiac output measurement techniques, J. CLIN. MONITORING 15:85–91 (1999)). The 95% confidence interval of the difference betweenrebreathing cardiac output and thermodilution cardiac output was between−1.19 and 1.08 L/min.

These comparisons evidence the accuracy with which pulmonary capillaryblood flow and cardiac output measurements may be obtained whenteachings of the present invention are employed.

Although the foregoing description contains many specifics, these shouldnot be construed as limiting the scope of the present invention, butmerely as providing illustrations of some of the presently preferredembodiments. Similarly, other embodiments of the invention may bedevised which do not depart from the spirit or scope of the presentinvention. Features from different embodiments may be employed incombination. The scope of the invention is, therefore, indicated andlimited only by the appended claims and their legal equivalents, ratherthan by the foregoing description. All additions, deletions andmodifications to the invention as disclosed herein which fall within themeaning and scope of the claims are to be embraced thereby.

1. A method for optimizing the accuracy of at least one of a carbondioxide elimination measurement obtained from a subject based on carbondioxide stores of a respiratory tract of the subject, comprisingapplying a filter comprising an algorithm that employs a transformationcoefficient based on carbon dioxide stores to a carbon dioxideelimination measurement of at least one breath by the subject and acarbon dioxide excretion estimate or carbon dioxide excretion signal forat least another breath.
 2. The method of claim 1, wherein applyingcomprises applying a filter comprising an algorithm that employs atransformation coefficient based on a functional residual capacity ofthe subject.
 3. The method of claim 1, wherein applying comprisesapplying a filter comprising an algorithm that employs a transformationcoefficient based on a functional residual capacity of the subject andan amount of carbon dioxide that has diffused into lung tissues.
 4. Themethod of claim 1, wherein applying comprises applying a low-passfilter.
 5. The method of claim 4, wherein applying the low-pass filtercomprises employing the following formula:(1−α){dot over (V)} _(M)CO₂(n)+α{dot over ({circumflex over (V)}_(B)CO₂(n−1), where {dot over (V)}_(M)CO₂(n) is the carbon dioxideelimination measurement, {dot over ({circumflex over (V)}_(B)CO₂(n−1) isan estimate of carbon dioxide excretion of another breath, and a is thetransformation coefficient based on an estimate of the carbon dioxidestores of the respiratory tract of the subject.
 6. The method of claim1, further comprising: estimating carbon dioxide excretion for the atleast another breath.
 7. The method of claim 6, wherein estimatingcarbon dioxide excretion for the at least another breath includesaccounting for carbon dioxide stores in the respiratory tract of thesubject during the at least another breath.
 8. The method of claim 7,wherein accounting for carbon dioxide stores comprises accounting forfunctional residual capacity during the at least another breath.
 9. Themethod of claim 7, wherein accounting for carbon dioxide storescomprises accounting for functional residual capacity and carbon dioxidewithin tissues of the respiratory tract during the at least anotherbreath.
 10. The method of claim 6, wherein estimating carbon dioxideexcretion of the at least another breath includes employing the formula:{dot over (V)}_(M)CO₂(n)+{circumflex over(V)}_(A)*(n)[f_(A)CO₂(n)−f_(A)CO₂(n−1)]RR, where {dot over(V)}_(M)CO₂(n) is the carbon dioxide elimination measurement for the atleast another breath, {circumflex over (V)}_(A)*(n) is an estimate of avolume of the carbon dioxide stores of the respiratory tract of thesubject during the at least another breath, [f_(A)CO₂(n)−f_(A)CO₂(n−1)]is a difference between a fraction of carbon dioxide in alveoli of therespiratory tract of the subject for the at least another breath and animmediately preceding breath, and RR is a respiratory rate of thesubject.
 11. The method of claim 1, further comprising determining anoptimal value for the transformation coefficient.
 12. The method ofclaim 11, wherein determining the optimal value comprises at least oneof iterative searching, rote searching, gradient searching, use of a setof predetermined equations, and adaptive filtering.
 13. The method ofclaim 11, further comprising, following the act of applying the filter,adjusting the estimate of carbon dioxide excretion of the at leastanother breath to improve a correlation between the carbon dioxideelimination measurement and an indicator of the content of carbondioxide in blood of the subject.
 14. A method for improving an accuracyof a respiratory signal, comprising: obtaining the respiratory signalfrom respiration of a subject during at least two breaths; and applyinga filter comprising an algorithm that employs a transformationcoefficient based on carbon dioxide stores of a respiratory tract of thesubject to the respiratory signal and measured or estimated respiratorydata from another breath.
 15. The method of claim 14, wherein applyingthe filter comprises applying a filter comprising an algorithm thatemploys a transformation coefficient based on functional residualcapacity of the respiratory tract.
 16. The method of claim 14, whereinapplying the filter comprises applying a filter comprising an algorithmthat employs a transformation coefficient based on functional residualcapacity of the respiratory tract and carbon dioxide in tissues of therespiratory tract.
 17. The method of claim 14, wherein applying thefilter comprises employing an estimate of at least one of a volume ofthe carbon dioxide stores of the respiratory tract of the subject and aflow of carbon dioxide into or out of the carbon dioxide stores.
 18. Themethod of claim 14, wherein obtaining the respiratory signal comprisesobtaining a carbon dioxide elimination signal from respiration of thesubject.
 19. The method of claim 18, wherein applying the filtercomprises employing the carbon dioxide elimination signal in thefollowing algorithm:(1−α){dot over (V)}_(M)CO₂(n)+α{dot over ({circumflex over (V)}_(B)CO₂(n−1), where {dot over (V)}_(M)CO₂(n) is the carbon dioxideelimination signal, {dot over ({circumflex over (V)}_(B)CO₂(n−1) iscarbon dioxide excretion and comprises at least a part of the measuredor estimated respiratory data from the another breath, and α is thetransformation coefficient.
 20. The method of claim 18, furthercomprising: estimating carbon dioxide excretion for the another breath.21. The method of claim 20, wherein estimating carbon dioxide excretionfor the another breath includes accounting for carbon dioxide stores inthe respiratory tract of the subject during the another breath.
 22. Themethod of claim 21, wherein accounting for carbon dioxide storescomprises accounting for functional residual capacity during the anotherbreath.
 23. The method of claim 21, wherein accounting for carbondioxide stores comprises accounting for functional residual capacity andcarbon dioxide within tissues of the respiratory tract during theanother breath.
 24. The method of claim 20, wherein estimating carbondioxide excretion of the another breath includes employing the formula:{dot over (V)}_(M)CO₂(n)+{circumflex over(V)}_(A)*(n)[f_(A)CO₂(n)−f_(A)CO₂(n−1)]RR, where {dot over(V)}_(M)CO₂(n) is the carbon dioxide elimination measurement for theanother breath, {circumflex over (V)}_(A)*(n) is an estimate of a volumeof the carbon dioxide stores of the respiratory tract of the subjectduring the another breath, [f_(A)CO₂(n)−f_(A)CO₂(n−1)] is a differencebetween a fraction of carbon dioxide in alveoli of the respiratory tractof the subject for the another breath and an immediately precedingbreath, and RR is a respiratory rate of the subject.
 25. The method ofclaim 14, further comprising determining an optimal value for thetransformation coefficient.
 26. The method of claim 25, whereindetermining the optimal value comprises at least one of iterativesearching, rote searching, gradient searching, use of a set ofpredetermined equations, and adaptive filtering.
 27. The method of claim25, further comprising, following the act of applying the filter,adjusting the estimate of carbon dioxide excretion of the at leastanother breath to improve a correlation between the carbon dioxideelimination measurement and an indicator of the content of carbondioxide in blood of the subject.
 28. A respiratory monitoring deviceconfigured to optimize the accuracy of a respiratory signal obtainedfrom at least one breath by a subject by accounting for carbon dioxidestores of a respiratory tract of the subject, comprising: at least oneprocessing element programmed to apply a filter comprising an algorithmthat employs a transformation coefficient based on carbon dioxide storesof a respiratory tract of the subject to the respiratory signal andmeasured or estimated respiratory data from another breath.
 29. Therespiratory monitoring device of claim 28, wherein the at least oneprocessing element is programmed to apply a filter comprising analgorithm that employs a transformation coefficient based on functionalresidual capacity of the respiratory tract.
 30. The respiratorymonitoring device of claim 28, wherein the at least one processingelement is programmed to apply a filter comprising an algorithm thatemploys a transformation coefficient based on functional residualcapacity of the respiratory tract and carbon dioxide in tissues of therespiratory tract.
 31. The respiratory monitoring device of claim 28,wherein the at least one processing element is programmed to apply afilter comprising an algorithm that comprises an estimate of at leastone of a volume of the carbon dioxide stores of the respiratory tract ofthe subject and a flow of carbon dioxide into or out of the carbondioxide stores.
 32. The respiratory monitoring device of claim 28,further comprising: at least one sensor for obtaining the respiratorysignal.
 33. The respiratory monitoring device of claim 32, wherein theat least one sensor is used to obtain a carbon dioxide eliminationsignal from respiration of the subject.
 34. The respiratory monitoringdevice of claim 33, wherein the at least one processing element isprogrammed to apply the following algorithm to the carbon dioxideelimination signal:(1−α){dot over (V)}_(M)CO₂(n)+α{dot over ({circumflex over(V)}_(B)CO₂(n−1), where {dot over (V)}_(M)CO₂(n) is the carbon dioxideelimination signal, {dot over ({circumflex over (V)}_(B)CO₂(n−1) iscarbon dioxide excretion and comprises at least a part of the measuredor estimated respiratory data from the another breath, and α is thetransformation coefficient.
 35. The respiratory monitoring device ofclaim 33, wherein the at least one processing element is also programmedto estimate carbon dioxide excretion for the another breath.
 36. Therespiratory monitoring device of claim 35, wherein, in estimating carbondioxide excretion for the another breath, the at least one processingelement is programmed to account for carbon dioxide stores in therespiratory tract of the subject during the another breath.
 37. Therespiratory monitoring device of claim 36, wherein the at least oneprocessing element is programmed to account for carbon dioxide storescomprising functional residual capacity during the another breath. 38.The respiratory monitoring device of claim 37, wherein the at least oneprocessing element is programmed to account for carbon dioxide storesfurther comprising carbon dioxide within tissues of the respiratorytract during the another breath.
 39. The respiratory monitoring deviceof claim 35, wherein the at least one processing element is programmedto apply formula to the carbon dioxide elimination measurement for theanother breath:{dot over (V)}_(M)CO₂(n)+{circumflex over(V)}_(A)*(n)[f_(A)CO₂(n)−f_(A)CO₂(n−1)]RR, where {dot over(V)}_(M)CO₂(n) is the carbon dioxide elimination measurement for theanother breath, {circumflex over (V)}_(A)*(n) is an estimate of a volumeof the carbon dioxide stores of the respiratory tract of the subjectduring the another breath, [f_(A)CO₂(n)−f_(A)CO₂(n−1)] is a differencebetween a fraction of carbon dioxide in alveoli of the respiratory tractof the subject for the another breath and an immediately precedingbreath, and RR is a respiratory rate of the subject.
 40. The respiratorymonitoring device of claim 28, wherein the at least one processingelement is programmed to determine an optimal value for thetransformation coefficient.
 41. The respiratory monitoring device ofclaim 40, wherein the at least one processing element is programmed toconduct at least one of an iterative search, a rote search, a gradientsearch, a set of predetermined equations, and adaptive filtering todetermine the optimal value.
 42. The respiratory monitoring device ofclaim 40, wherein the at least one processing element is programmed toadjust the estimate of carbon dioxide excretion of the at least anotherbreath to improve a correlation between the carbon dioxide eliminationmeasurement and an indicator of the content of carbon dioxide in bloodof the subject following application of the filter.